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Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Mathematics3D Coordinate GeometryCoordinates of a point in space, Direction cosines,Medium2 minQB

MathematicsMediumsingle choice

If $A (0, 1, 2), B (2, - 1, 3)$ and $C (1, - 3, 1)$ are the vertices of a triangle, then its circumcentre and orthocentre are situated at a distance of

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Solution:

$B A \cdot BC = (- 2, 2, - 1) \cdot (- 1, - 2, - 2) = 0$ , so the angle at B is a right angle. Orthocentre = $B (2, - 1, 3)$ . Circumcentre = midpoint of $AC = (\frac{1}{2}, - 1, \frac{3}{2})$ . Distance $= \frac{9}{4} + \frac{9}{4} = \frac{3}{2}$ .

Stream:JEESubject:MathematicsTopic:3D Coordinate GeometrySubtopic:Coordinates of a point in space, Direction cosines,

⏱ 2mℹ️ Source: QB

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